(where \(\alpha \)  is a parameter which we set by cross validation).
This penalises labellings \(L = \lbrace l_1,...,l_T\rbrace \)  which are not smooth, thus enforcing a piecewise constant solution.
All contiguous sub-sequences form the desired activity proposal (which can be as many as there are instances of activities).
Each activity proposal is assigned a global score \(S_a\)  equal to the mean of the scores of its constituting frames.
This optimisation problem can be efficiently solved by dynamic programming [1]}.
It can easily be extended for simultaneous detection and classification [1]}.
